Simplifying Rational (Fractional) Expressions To simplify an algebraic fraction means to reduce it to lowest terms. This is done by dividing out the common factors in the numerator and the denominator. Read more: Adding and Subtracting Rational (Fractional) Expressions Multiplication of Rational (Fractional) Expressions Division of Rational (Fractional) … [Read more...] about Simplifying Rational (Fractional) Expressions
CoFunctions
CoFunctions Such examinations, lead us to three sets of "cofunction" identities: Also written: Notice the connection of the letters C & O: * sine and cosine cofunctions * tangent and cotangent cofunctions * secant and cosecant cofunctions * complementary Examples: 1. Find a Value of θ for which sin θ = cos 15º is true Solution: Since sine and … [Read more...] about CoFunctions
Using Transformations to Investigate Functions
Using Transformations to Investigate Functions Let's investigate how transformations may be applied to functions: Example 1: Remember to utilize your graphing calculator to get a feel for the function and the changes. Transform the function f (x) = ex with a vertical stretch by a factor of 3, followed by a translation 5 units to the right. Write an equation for the … [Read more...] about Using Transformations to Investigate Functions
Graphs of the Inverse Trig Functions
Graphs of the Inverse Trig Functions When we studied inverse functions in general (see Inverse Functions), we learned that the inverse of a function can be formed by reflecting the graph over the identity line y = x. We also learned that the inverse of a function may not necessarily be another function. Look at the sine function (in red) at the right. If we reflect this … [Read more...] about Graphs of the Inverse Trig Functions
The Graphs of y = tan(x), y = sec(x), y = csc(x), y = cot(x)
The Graphs of y = tan(x), y = sec(x), y = csc(x), y = cot(x) Graphs of trigonometric functions can be produced in degrees or in radians. The graphs appearing here will be done in radians. Hint: When hand-drawing the graphs of sine and cosine, draw vertical dotted lines at intervals to remind you of the connection to the quadrants from the unit circle and to keep your … [Read more...] about The Graphs of y = tan(x), y = sec(x), y = csc(x), y = cot(x)